Your yoni is an animal temperament, and you do not choose it: it comes from the nakshatra the Moon occupied when you were born. Twenty-seven nakshatras share fourteen animals between them, each animal usually holding one male nakshatra and one female, which is why two people can share a yoni and still differ.
Classical matching uses yoni to read the instinctive, physical layer of a partnership, the part that has little to do with values or conversation. It is one of the eight kutas of Ashtakoot, worth four points, and the seven enmity pairs below are where it deducts them.
Yoni is not BNN. Bhrigu Nandi Nadi reads a partnership through karakas, yutis and yatra timing, not through Ashtakoot points. Yoni is published here as classical reference. For the BNN view of a match, use BNN Match.
Don't know your yoni? Generate your free chart → It is shown under Basic Details and again under Beyond BNN.